To say the <h> tags are non-essential is incorrect. The textual hierarchy of your content should be defined by <h> tags because the search engines use the <h> tag to better index the content of your site.
Matches between meta-tags and <h> tags in your text are invaluable for indexing, especially for deep searches which will become the internet norm.
Think <h> tags with you are putting text on your site - particularly when it matches anything in your meta-tags.